On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

In this paper, we present a numerical technique for solving fractional Sturm–Liouville problems with variable coefficients subject to mixed boundary conditions. The proposed algorithm is a spectral Galerkin method based on fractional-order Legendre functions. Tedious manipulation of the series appearing in the implementation of the method have been carried out to obtain a system of algebraic equations for the coefficients. Our findings demonstrate the possibility of having no eigenvalues, finite number of eigenvalues or infinite number of eigenvalues depending on the fractional order. The convergence and effectiveness of the present algorithm are demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)261-267
Number of pages7
JournalChaos, Solitons and Fractals
Volume116
DOIs
Publication statusPublished - Nov 2018

Keywords

  • Caputo derivative
  • Eigenvalues and eigenfunctions
  • Fractional Legendre functions
  • Fractional Sturm–Liouville problems
  • Spectral methods

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems'. Together they form a unique fingerprint.

Cite this